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Applications of Cross Product

The vector ar...

Question

The vector area of the triangle with vertices $^i +^j +^k,^i +^j + 2^k,^i + 2^j +^k$ is

A

^i

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B

-^i

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C

\frac{1}{2} i

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D

- \frac{1}{2} i

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Solution

The correct option is D $- \frac{1}{2} i$
$- - \to A B = - - \to O B - - - \to O A =^k, - - \to A C = - - \to O C - - - \to O A =^j$ . Vector area = $\frac{1}{2} (- - \to A B \times - - \to A C) = \frac{1}{2} (k \times^j) = - \frac{1}{2}^i$ .

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